Chapter 4.6, Problem 1CE

To determine

To prove: the angle $\overline{AS}\cong \overline{DT}$ with the help of given information.

Answer to Problem 1CE

The angle $\overline{AS}\cong \overline{DT}$ is proved.

Explanation of Solution

Given information:

The system information:

  $\text{Δ}ABC\cong \text{Δ}DEF$

  $\angle C\cong \angle F$

  $\text{Δ}ACS\cong \text{Δ}DFT$

Given diagram:

  

  

Calculation:

Key steps of proof are as follows:

a. $\text{Δ}ABC\cong \text{Δ}DEF$ (Side-Angle-Side Postulate)

b. $\angle C\cong \angle F$ (Corresponding $\angle$ s of $\cong \text{Δ}$ are $\cong )$

c. $\text{Δ}ACS\cong \text{Δ}DFT$ (Side-Angle-Side Postulate)

d. $\overline{AS}\cong \overline{DT}$ (Corresponding parts of $\cong \text{Δ}$ are $\cong )$